Newton and Secant Methods for Iterative Remnant Control of Preisach Hysteresis Operators

TL;DR

This paper introduces Newton and secant iterative methods for controlling the remnant state in Preisach hysteresis models, improving convergence speed for energy-efficient piezoactuator control.

Contribution

It proposes novel Newton and secant update laws for remnant control in Preisach hysteresis, demonstrating faster convergence than existing methods.

Findings

Remnant curve is monotonically increasing with positive weights.

Newton and secant methods outperform existing algorithms in convergence speed.

Numerical simulations validate the improved control performance.

Abstract

We study the properties of remnant function, which is a function of output remnant versus amplitude of the input signal, of Preisach hysteresis operators. The remnant behavior (or the leftover memory when the input reaches zero) enables an energy-optimal application of piezoactuator systems where the applied electrical field can be removed when the desired strain/displacement has been attained. We show that when the underlying weight of Preisach operators is positive, the resulting remnant curve is monotonically increasing and accordingly a Newton and secant update laws for the iterative remnant control are proposed that allows faster convergence to the desired remnant value than the existing iterative remnant control algorithm in literature as validated by numerical simulation.